a high-level signal integrity fault model and test

Abstract—In this paper, considering the interconnection topology information, an abstract model and a new test pattern generation method of signal integrity problems on interconnects are proposed. In addition, previous SPICE-based pattern generation methods are too complex and time consuming to generate test patterns for signal integrity faults. To more accurately detect signal integrity defects on practical on-chip interconnection lines and avoid time consuming for interconnection analysis, in this paper, we propose a new high-level signal integrity fault model to estimate noise effects based on process variation and interconnect signal transition. Experimental results show that the proposed signal integrity fault model is more exact for long interconnects than previous approaches. In addition, the proposed method is much faster than the SPICE-based pattern generation method.

I. INTRODUCTION Signal integrity issues arise from long on-chip

interconnects where the effect of parasitic elements may jeopardize the functionality and reliability of high performance SoCs. Long on-chip interconnects fall primarily into three categories: data-buses, control, or clock. Data lines, especially those such as data buses between the central processing unit (CPU) and cache, travel in groups, generally have half-a-chip-edge in length, and have a small load at the receiver. Such lines synchronously operate and are designed for minimum path delay over fairly long length. Therefore, these data-buses are vulnerable to signal integrity problems due to their synchronous and possibly in-phase data pattern. Therefore, in this paper, we focus on testing signal integrity faults on long interconnects like data-buses.

To enable testing for signal integrity defects, several fault models and test generation methods have been proposed to capture the signal integrity effects in gate-level circuits [1-3]. In addition, many approaches for analysis, modeling and testing signal integrity effects on long interconnect have been proposed [4-7]. Maximum Aggressor (MA) fault model was presented in [4], which abstractly models crosstalk effects on interconnects with a linear number of faults. Although MA significantly simplifies the problem for interconnects modeled as RC circuits, it suffers from lack of precision needed for accurate RLC interconnect models [8]. In [5], the authors presented a BIST for signal integrity using pseudo-random patterns. Signal integrity fault model was presented in [9]. This was based on accurate RLC interconnect models;

however, this method requires much large computation power for solving numerical equations.

Moreover, since previous works [1-9] did not consider the effect of interconnection topology, their accuracy is much more decreased. For the effect of interconnection topology, in general, the SPICE-based simulation is necessary. However, the SPICE-based simulation is prohibitively time consuming and are unsuitable for iterative evaluations of SoCs. To alleviate this problem and to generate more effective test patterns for signal integrity faults, we already proposed the high-level test pattern generation method with the consideration of the interconnection topology in [10]. In general, the proposed fault model in [10] is efficient to simply generate test patterns for signal integrity faults with a slight error. However, for high-speed VLSI circuits, high-level signal integrity fault model presented in [10] is not sufficient to accurately detect signal integrity defects on practical long interconnections because it cannot consider physical phenomenon of practical on-chip interconnection lines.

To more accurately detect signal integrity defects on practical on-chip interconnection lines and avoid time consuming for interconnection analysis, in this paper, we propose a new high-level signal integrity fault model to estimate noise effects based on process variation and interconnect signal transition. Especially, for signal integrity-induced delay errors, the proposed high-level fault models are based on TWA (traveling wave based waveform approximation) technique for multi-coupled interconnects. In addition, the proposed test pattern generation for a novel high-level fault model for signal integrity faults is proposed considering the interconnection topology in the similar manner of [10].

The rest of the paper is organized as follows. Section 2 explains the signal integrity effects on long on-chip interconnection lines and two main errors caused by signal integrity noises. In Section 3, new high-level fault models for signal integrity-induced errors are proposed and Section 4 provides the proposed test pattern generation algorithm. Experimental results are presented in Section 5 and this paper is concluded in Section 6.

II. SIGNAL INTEGRITY EFFECTS ON LONG INTERCONNECTS According to [11], the short local wiring with the highest

A High-level Signal Integrity Fault Model and Test Methodology for Long On-Chip Interconnections

Sunghoon Chun1, Yongjoon Kim1, Taejin Kim2 and Sungho Kang1 1Department of Electrical and Electronic Engineering Yonsei University

134 Shinchon-dong Seodaemoon-gu, Seoul, Korea E-mail: <shchun, yjkim, shkang>@yonsei.ac.kr

2Avionics R&D Lab., LIG Nex1 Co. 100 Shinsungdong Yoosung-gu, Daejeon, Korea

E-mail: [email protected].

2009 27th IEEE VLSI Test Symposium

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Authorized licensed use limited to: Yonsei University. Downloaded on October 22, 2009 at 21:48 from IEEE Xplore. Restrictions apply.

density and R>500Ω/cm are found useful for lengths less 3mm. As the scaling to smaller dimensions continues, the short wires will have resistance several times this value, but their behavior will stay the same. Their capacitance and capacitive coupling to adjacent neighbors are the limiting factors due to delay and delay variation. The medium-length lines with 100<R<500Ω/cm can be used for lengths up to 10mm if driven by low-impedance drivers and have wide line-to-line separations that result in low crosstalk. This is especially important as noise budgets are shrinking. Smaller devices use lower Vdd levels that could generate lower noise. However, signal transitions are faster, thus resulting in higher noise budgets are shrinking. In addition, processing tolerances for both the devices and the interconnect layers and larger Vdd variation result in overall noise budget reduction. Noise sources also have a higher probability of overlapping within the shorter cycle-time windows. Based on analysis of [11], the main noise capacitance is not excessive. The additional noise is generated by the mutual inductance term. The longer lines, such as data-buses, control and clock lines, with R<100Ω/cm, can propagate fast signals for lengths greater than 100mm. The circuit representation which accounts for both capacitance and inductive coupling is essential for correctly estimating the crosstalk noise. Since we develop a more accurate and simpler fault model for crosstalk for long interconnects in a system-on-chip, both capacitance and inductance are considered.

In a multiple wire system, the signal transitions on neighboring wires generate crosstalk-induced noise through the coupling capacitances and the mutual inductances between wires. In this section, I define the affecting wires as aggressors and the affected wires as victims. In general, crosstalk-induced noise is broadly classified into two types. Glitch noise [12] occurs when a victim line is intended to be at a stable state and results in an unwanted noise pulse on the net. Delay noise [13] occurs when noise is injected on a net when it transitions, and results in a change in the delay of the net.

III. HIGH-LEVEL SIGNAL INTEGRITY FAULT MODELS

A. High-Level Fault Model for Delay Noise Errors For high-speed long interconnection systems, the time

domain response is roughly approximated by two or three poles. However, since the on-chip interconnection signal changes abruptly during the transition due to the inductance and the reflection, the time domain response cannot be accurately modeled with three or more poles. Therefore, the voltage signal is better physically represented using traveling wave concepts.

To accurately model the voltage signal using physical phenomena, in the TWA-technique [14], the low frequency transient signal is represented with three-dominant poles and the high frequency characteristics of the transient signal are incorporated into an approximation function by exploiting the traveling wave characteristics and a modified RC-response

approximation in the time domain. When the load is open circuit, the response wave becomes

at double the incident wave. But, there are many frequency components from dc to very high frequency in a pulsed signal. In addition, since the load has a capacitive reactance and this impedance depends on the frequency, the reflection coefficient is inherently frequency-dependent. Since the sharp edge of the time domain voltage response which is the summation of the incident and reflected waves is blunt a bit, therefore, the response wave can be depicted by the combination of a linear ramp shape and a RC-like behavior wave shape.

In this case, the first incident wave arrives at the load with the time of the flight (tf1) of a wave that is as follows.

(1)

where Lline is the inductance of line and Cline is the capacitance of the line. In this case, including the load capacitance CL, an effective time of flight (tf0) is approximated as follows.

(2)

Thus, the effective response time delay (δ) of the incident wave due to the capacitive load is defined as follows.

(3)

According to [14], in the time interval between (2n-1)tf0-δ and (2n-1)tf0+δ, where n= 1,2,3,…, the waveform can be approximated with a linear function. In contrast, in the time interval between (2n-1)tf0+δ and (2n+1)tf0+δ, the waveform can be modeled with an RC-response-like function. The time constant can be reasonably modeled as follows [14].

(4) In [14], the output voltage function is approximated for

three coupled lines. This technique can extend to the output waveform modeling for multi-coupled lines [15]. The traveling waves of n-coupled on-chip interconnection lines can be decoupled into the linear combination of the n-eigenmodes by using a modal analysis technique in the frequency domain if the lines are identical [16-17]. Using these decoupling information and the TWA approximation, the output voltage waveform can be approximated easily [15].

Although the TWA-based output voltage function is very accurate, for the high-level signal integrity fault modeling, it is not necessary to calculate entire output voltage values of the victim line because it is very time consuming. Therefore, we propose a new high-level signal integrity fault model using the TWA-based waveform function [14, 15].

For slowdown and speedup fault models, the time delay is estimated when the output voltage of the victim line reaches 50% of the transition voltage. Timing delay of the output signal depends heavily on the changes of the total line inductance and the total line capacitance, which are related to the signal patterns. Since a linear combination of n eigenmodes of the system depends on the signal patterns, the signal voltage and the time delay for each signal pattern is

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different. In this case, the time delay for each signal pattern mode is defined to td(k), where k indicates the kth signal pattern mode.

Figure 1. Modeling for a signal integrity-induced delay noise

Comparing the SPICE simulation and the TWA-based

waveform approximation and analyzing their results, as shown in Fig. 1, we can find out that the 50% time delay occurs in the time interval between (2n-1)tf0-δ and (2n-1)tf0+δ (the period of the linear function). A signal voltage function is modeled with the consideration of all the frequency components from dc to high frequency. In this case, since the reflection coefficient of low frequency components is close to one, most of the low frequency components may be reflected at the capacitive load. Therefore, the effects of the low frequency components will make signal transition fast because the low frequency components contain the major part of the signal energy and the reflections are appeared in the time interval between (2n-1)tf0-δ and (2n-1)tf0+δ. In this abrupt transient time, the signal voltage can be modeled with the linear function and then the signal voltage will reach 0.5 Vdd in this time interval. Therefore, we can claim that the 50% time delay occurs in the following condition.

(5) In this condition, to accurately the 50% time delay value, it

is necessary to calculate the linear output voltage function in [14]. The 50% delay of the victim line can be determined by letting the linear output voltage function be 0.5 Vdd. That is like the equation (6).

However, it is not necessary to calculate the equation (6) in order to determine whether a crosstalk-induced delay fault exists in the victim line or not. Since the time interval of the 50% time delay condition in the linear function is very short and the value of the voltage output function changes abruptly, the 50% time delay can be expected through calculating just the values of tf1 and tf0+δ(k). Note that the values of tf1 and tf0+δ(k) can be calculated by using the equation (1), (2) and (3). Note that the total inductance and the total capacitance of the victim line in the equations (1), (2) and (3) are as follows.

(7)

(8)

where Aj is the polarity of the coupling parameters. In addition, though the analysis of the SPICE output response and the TWA-based waveform in the linear output voltage function, we can find out that most 50% time delay occurs during the following time interval.

(9) In this condition, the 50% time delay can be approximated

to α(tf0+δ(k)), where 0.7 ≤ α ≤ 0.9, since the criterion of the crosstalk-induced delay is just required to determine whether crosstalk-induced error can occur in the victim line or not. Therefore, for slowdown delay, if the approximated 50% time delay is equal to or larger than the threshold delay value tdth, a slowdown error will occur. From the approximated 50% time delay, td50%(k), we can identify whether the slowdown error occurs in the victim line or not. The criterion of the slowdown delay fault, DFRsd is as follows.

(10)

where α is an user defined value based on the manufacturing process. In this paper, we use α=0.9 for experiments.

Based on the monotone property, the larger the delay factor ratio is, the larger a signal integrity noise will be generated. Therefore, we can determine whether the noise is large enough to cause an error from the delay factor ratio without the SPICE simulation. Similarly, speedup signal integrity error effects can be estimated and generated.

B. High-Level Fault Model for Glitch Noise Errors For multiple interconnections, the signal integrity noises

caused by the electric and magnetic fields depend on the signal patterns. Therefore, we should consider the signal directions to derive a high-level signal integrity noise model.

Figure 2. An example of two coupled interconnections

First, let’s consider an odd mode signal propagation for

(6)

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two interconnects. The odd mode propagation occurs when

two coupled transmission lines are driven with equal

magnitude and 180° out of phase with one another. In odd

mode propagation, the currents on the lines, I1 and I2, always

are driven with equal magnitude but in opposite directions

(Fig.2). Assume that the self-inductances and self-capacitances are different values according to the length of

interconnections and the mutual inductances and coupling

capacitances are extracted through the parasitic extraction

tools. Applying Kirchhoff’s voltage law produces

(11)

(12)

Since the signals for odd mode switching are always

opposite, it is necessary to substitute I1=-I2 and V1=-V2 into

the equations (11) and (12). Therefore, the equivalent

inductance in a pair of coupled transaction lines propagating

in odd mode is (13)

Similarly, the effect of the coupling capacitance can be

derived by applying the Kirchhoff’s current law. The

equivalent capacitance in a pair of coupled interconnection

propagating in odd mode is (14)

Subsequently, the equivalent impedance for a coupled pair

of interconnection propagating in an odd mode pattern is

(15)

Next, we consider an even mode signal propagation for

two interconnects. The even mode propagation occurs when

two coupled interconnections are driven with equal

magnitude and are in phase with one another. The even mode

transmission characteristics for a coupled two line system are

derived in the similar manner for the odd mode.

(16)

This can be expanded to determine the effective

impedance and variations induced by the signal integrity of

multiple interconnection systems. For n interconnections, the

effective impedance factor is as follows.

(17)

In this case, including resistance in the analysis of the

interconnect line adds significant complexity to the problem

and the resulting equations and fault models fail to provide

much physical insight. For simplicity, a low-loss

approximation [18] is used to include the effect of line

resistance in the above equation (17). In a low-loss

approximation (R < 2Zi,eff), since a voltage step traveling

along a interconnect line of characteristic impedance is

attenuated by a factor of [18], the characteristic impedance factor value for lossless line, Zi,eff(lossless) is attenuated by the same factor. Based on this theory, using the following equations, the characteristic impedance factor of lossless lines can be computed.

(18) For positive glitch error, if the reciprocal of the effective

impedance factor value is equal to or larger than the reciprocal of the threshold impedance value ZFth, a positive glitch error will occur. Therefore, from the impedance factor ratio ZFRpg, we can identify whether the positive glitch error occurs in the victim line or not. The ZFRpg is as follows.

(19)

C. High-Level Signal Integrity Fault Models Using above criterions of crosstalk-induced errors, we can

determine whether the noise is large enough to cause an error without the SPICE simulation. Similarly, other signal integrity-induced error effects can be estimated and generated. Table 1 shows the proposed high-level signal integrity fault models obtained from the criterion of each signal integrity error. Note that the impedance factor ratio is in inverse proportion to the signal integrity-induced voltage.

Table 1. High-level signal integrity fault models

Signal Integrity Fault

Pattern of Victim Line

High-Level Fault Model

Positive Glitch Stable 0

Negative Glitch Stable 1

Rising Slowdown Rising Transition

Falling Slowdown Falling Transition

Rising Speedup Rising Transition

Falling Speedup Falling Transition

ZFR: the impedance factor ratio, DFR: the delay factor ratio

IV. TEST PATTERN GENERATION FOR HIGH-LEVEL SIGNAL INTEGRITY FAULTS

The proposed test pattern generation, called High-SI (High-level Signal Integrity fault test pattern generation) is shown in Fig. 3.

For a given interconnect system, an RLC network is generated by using parasitic extraction tool with process technology libraries and the modal decoupling [16-17]. Next,

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a victim line is selected from the list of possible victims and then the interconnection topology graph for the selected victim line is generated. In [10], we already proposed the interconnection topology graph to consider the impact of the length of the aggressor coupled to the victim line. Using the topology graph with the effective length and the distance, the effective test patterns for crosstalk faults can be generated with the consideration of the impact of the interconnect topology.

After generating the topology graph, the limited factor for the selected victim line is determined by calculating the impedance factor ratio and the delay factor ratio with the topology graph. Using this information, the desired test vector pair for the proposed fault model can be produced.

Until the list of possible victim lines is empty, the above test pattern generation procedures are continued. The generated test patterns for our proposed fault model consists of a single victim, the limited number of aggressors whose dominant aggressor source is the coupling capacitance and other aggressors whose mutual inductances affect crosstalk-induced errors on the victim line more dominantly.

Figure 3. Overall algorithm of the proposed test pattern generation

V. EXPERIMENTAL RESULTS The proposed high-SI test generation method is validated

by the use of HSPICE simulations [19]. For first experiment, a symmetric 8-bit interconnection line is used to compare the test pattern generated by the high-MX test generation, the MA test pattern [4] and the MT test pattern [7]. The on-chip interconnection line parameters for the first experiment are as follows: the resistance of 68.966Ω/cm, the self-inductance of 7.214nH/cm and the self-capacitance is 2.432pF/cm. Since the mutual inductances and the coupling capacitances depend on the distance between the coupled lines, all values are not explained in this section. For example, the coupling capacitance and the mutual inductance between the aggressor line 1 and the victim line are 0.532 pF/cm and 5.115 nH/cm, respectively. In addition, all the source resistances are assumed to be 50Ω and all the load capacitances are assumed to be 0.1pF. Assuming that the victim line is the line 4 in the 8-bit interconnection line, the HSPICE simulation result of each test pattern for the rising slowdown delay is shown in Fig. 4.

As shown in Fig. 4, the proposed high-SI test generation method can generate more highly effective test patterns than previous works. The MA fault model [4] tended to underestimate noise errors due to the RC interconnect model. When mutual inductance comes into play, the MA fault model [7] may not have reflected the worst case and caused other ways to generate test patterns to create maximal integrity loss. In addition, although the MT fault model can lead to generate more effective test patterns than the MA fault model, many test patterns for a single MT fault model are required because the test patterns for aggressor lines excluding the limited lines are generated randomly. The waveform for the MT test pattern in Fig. 4 shows the worst case of the randomly generated MT test patterns. Therefore, as shown in the result of the HSPICE simulation, the proposed high-SI fault model can lead to generate more effective test patterns which cause more crosstalk-induced noises.

For the second experiment, we use 8-bit interconnection that has randomly generated topology in a 0.18µm process, and assume that the line 4 is a victim line. Note that the tool FASTHENRY was used for extracting inductance values [20] and the interconnect parameters are as follows: the resistance of 0.1Ω/µm, the self-inductance of 0.6pH/µm and the mutual

Figure 4. Slowdown delays of the proposed method and previous works

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inductance of 0.4pH/µm are considered. In addition, the capacitance is 0.185fF/µm and the coupling capacitance is 0.064fF/µm. Interconnection length of 1000µm is considered.

Using 8, 16 and 32 interconnection systems with randomly generated interconnection topologies, running for 3mm in parallel on metal layer 4, and in a 0.18 µm process, we demonstrated the efficiency of the high-SI test generation with the interconnection topology graph. In addition, we perform experiments for AHB and APB bus in our ARM-based Network Processor. Table 2 shows the defect coverage percentages for the MA test patterns [4], MT test patterns [7] and test patterns generated by the high-SI method with the interconnection topology. As shown in Table 2, among the three test vector sets, the high-SI test generation method with the interconnection topology is the most efficient for all the interconnect systems. In addition, the high-SI method significantly reduces time to generate test patterns for signal integrity faults than the SPICE-based pattern generation method.

TABLE 2. COMPARISON OF VARIOUS INTERCONNECT SYSTEMS BUS MA [4] MT [7] High-SI

8bit (1) 81% 86% 96% 8bit (2) 84% 91% 98% 8bit (3) 77% 84% 93%

16bit (1) 72% 77% 90% 16bit (2) 75% 75% 87% 16bit (3) 81% 83% 86% 32bit (1) 64% 80% 91% 32bit (2) 72% 83% 92% 32bit (3) 68% 75% 90%

AHB 54% 68% 87% APB 58% 65% 91%

VI. CONCLUSION To more accurately detect signal integrity defects on

practical on-chip interconnection lines and avoid time consuming for interconnection analysis, in this paper, we propose a new high-level signal integrity fault model to estimate noise effects based on process variation and interconnect signal transition. Especially, for signal integrity-induced delay errors, the proposed high-level fault models are based on TWA (traveling wave based waveform approximation) technique for multi-coupled interconnects.

The proposed high-SI test pattern generation is based on the analysis of the impact of aggressor lines on signal integrity effect at a victim line. We then presented a methodology to deal with arbitrary interconnect topologies. Using the interconnection topology graph and two factors, the DFR and the ZFR, our methodology generates test vector pairs to maximize the impact of aggressor lines.

Experimental results showed that the proposed high-SI test patterns are more exact than the MA and the MT patterns and the defect coverage is much higher since the MA fault model leads to underestimation of signal integrity effects due to the RC network and the MT patterns are randomly generated.

Currently, there is ongoing research to develop a BIST

methodology to efficiently apply test vectors for the high-SI fault model.

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